High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

What is the Most Effective Method of Error Correction in L2 Writing?

The efficacy of error correction and various kinds of correction approaches is one of the key issues in second language writing faced by both teachers and researchers. The current paper reviews the definition of error correction and examines the different views on whether error correction in L2 writing should be corrected. In particular, the paper discusses and analyses the three common correction methods: direct correction, peer feedback and indirect correction. Teachers are encouraged to weigh and analyze the advantages and disadvantages of these methods according to the current literature, employ the most beneficial error correction method in L2 writing, and adapt its suitability to their teaching context.

A Correction Method Suitable for Dynamical Seasonal Prediction

Based on the hindcast results of summer rainfall anomalies over China for the period 1981-2000 by the Dynamical Climate Prediction System （IAP-DCP） developed by the Institute of Atmospheric Physics, a correction method that can account for the dependence of model＇s systematic biases on SST anomalies is proposed. It is shown that this correction method can improve the hindcast skill of the IAP-DCP for summer rainfall anomalies over China, especially in western China and southeast China, which may imply its potential application to real-time seasonal prediction.

Low/distortion on Exterior Surface of Auto Body and Its Correction Method

Surface low/distortion is one of the most challenging surface deflections that have a great effect on the exterior appearance of automobiles.Most studies on surface distortion/deflection have focused on evaluation and visualization techniques,the research work on correction or prevention of surface low/distortion is limited,and there is no perfect surface low/distortion corrective method that can satisfy the needs of the engineering.A B-spline based geometry morphing algorithm is proposed and then a new program based on UG-NX platform is developed to modify the die face in the surface low/distortion areas.To verify this developed system,the experimental dies that can replicate the surface low/distortion phenomenon successfully is put to use.Five geometric variables are introduced to describe the basic geometry of typical depression features of automotive outer panels.The experimental dies are then designed to reflect various combinations of these geometric parameters.The stamping experiments are conducted on cold rolled grade 5（CR5） sheet steel and various static measurements,such as oil-stoning,laser scanner,etc,are performed to measure and record the surface low/distortions.Three approaches including good bearing,holds in blank and die face morphing that aim to correct low/distortions are tried out and surface low/distortions are observed in the specimen with reverse draw depth of 10 mm.The measurement results show that die morphing is a practical and effective method to correct the surface low/distortion.The correction method proposed can be used to minimize the occurrence of surface low/distortion in die manufacturing,which has certain reference significance to the correction of surface low/distortion.

Analogue correction method of errors and its application to numerical weather prediction

In this paper, an analogue correction method of errors （ACE） based on a complicated atmospheric model is further developed and applied to numerical weather prediction （NWP）. The analysis shows that the ACE can effectively reduce model errors by combining the statistical analogue method with the dynamical model together in order that the information of plenty of historical data is utilized in the current complicated NWP model, Furthermore, in the ACE, the differences of the similarities between different historical analogues and the current initial state are considered as the weights for estimating model errors. The results of daily, decad and monthly prediction experiments on a complicated T63 atmospheric model show that the performance of the ACE by correcting model errors based on the estimation of the errors of 4 historical analogue predictions is not only better than that of the scheme of only introducing the correction of the errors of every single analogue prediction, but is also better than that of the T63 model.

Types and Correction Methods of Matrix Effect during Zircon LA-ICP-MS U-Pb Dating

Matrix effect primarily impacts the accuracy and precision of zircon LA-ICP-MS U-Pb data.This paper describes three types of matrix effect in zircon LA-ICPMS U-Pb dating,i.e.,the element matrix effect,high Ddpa or uranium matrix effect and alpha dose matrix effect,and illustrates the correction of these three effects.In addition,we point out the limitation and possible problems of the existing correction methods.

PPA BASED PREDICTION-CORRECTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES

In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a correction using the PPA formula. We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions.

ON THE METHODS FOR FINDING ROOTS OF ALGEBRAIC EQUATIONS WITH WEIERSTRASS' CORRECTIONS

This is a study of the Durand-Kerner and Nourein methods for finding the roots of a given algebraic equation simultaneously. We consider the conditions under which the iterative methods fail. The numerical example is presented.

New Estimates for the Rate of Convergence of the Method of Subspace Corrections

We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections.

An Improved Method for Correction of Air Temperature Measured Using Different Radiation Shields

The variation of air temperature measurement errors using two different radiation shields （DTR502B Vaisala,Finland,and HYTFZ01,Huayun Tongda Satcom,China） was studied.Datasets were collected in the field at the Daxing weather station in Beijing from June 2011 to May 2012.Most air temperature values obtained with these two commonly used radiation shields were lower than the reference records obtained with the new Fiber Reinforced Polymers （FRP） Stevenson screen.In most cases,the air temperature errors when using the two devices were smaller on overcast and rainy days than on sunny days; and smaller when using the imported rather than the Chinese shield.The measured errors changed sharply at sunrise and sunset,and reached maxima at noon.Their diurnal variation characteristics were,naturally,related to changes in solar radiation.The relationships between the record errors,global radiation,and wind speed were nonlinear.An improved correction method was proposed based on the approach described by Nakamura and Mahrt （2005） （NM05）,in which the impact of the solar zenith angle （SZA） on the temperature error is considered and extreme errors due to changes in SZA can be corrected effectively.Measurement errors were reduced significantly after correction by either method for both shields.The error reduction rate using the improved correction method for the Chinese and imported shields were 3.3％ and 40.4％ higher than those using the NM05 method,respectively.

ANALYSIS OF HUMAN PLACENTA BY ^(31)P NUCLEAR MAGNETIC RESONANCE AND THIN-LAYER CHROMATOGRAPHY SCANNING COMBINED WITH THE CORRECTIVE METHOD OF ABSORBANCE PROPORTIONAL COEFFICIENT

Five phospholipids in human placenta were determined by phosphorus 31 nuclear magnetic resonance(^(31)P NMR)spectroscopy and thin-layer chromatography(TLC) scanning combined with the corrective method of absorbance proportional coefficient. The NMR spectrometer used this investigation was a Bruker AM-500 spectrometer operating at 202.4 MHz for ^(31)P chemical shifts are relative to 85% phosphoric acid. TIC was carried out by silica gel H plate developed in chloroform-methanol-glacial acetic acid-ethanol-water(25:4:6:2:0.5),with Vaskovsky reagent as colour -developing agent of phospholipids.

Accuracy of the half-power bandwidth method with a third-order correction for estimating damping in multi-DOF systems

A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth method with the third-order correction in damping estimation for multi-DOF linear systems.Damping ratios in a two-DOF linear system are estimated using its displacement and acceleration frequency response curves,respectively.A wide range of important parameters that characterize the shape of these response curves are taken into account.Results show that the third-order correction may greatly improve the accuracy of the half-power bandwidth method in estimating damping in a two-DOF system.In spite of this,the half-power bandwidth method may significantly overestimate the damping ratios of two-DOF systems in some cases.

Correction of cosine oscillation to the improved correlation method of estimating the amplitude of gravitational background signal

In the measurement of G with the angular acceleration method,the improved correlation method developed by Wu et al.（Wu W H,Tian Y,Luo J,Shao C G,Xu J H and Wang DH 2016 Rev.Sci.Instrum.87 094501） is used to accurately estimate the amplitudes of the prominent harmonic components of the gravitational background signal with time-varying frequency.Except the quadratic slow drift,the angular frequency of the gravitational background signal also includes a cosine oscillation coming from the useful angular acceleration signal,which leads to a deviation from the estimated amplitude.We calculate the correction of the cosine oscillation to the amplitude estimation.The result shows that the corrections of the cosine oscillation to the amplitudes of the fundamental frequency and second harmonic components obtained by the improved correlation method are within respective errors.

PARALLEL ALGORITHMS OF ONE-LEG METHOD AND ITERATED DEFECT CORRECTION METHODS

The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.

A Gas Dynamics Method Based on the Spectral Deferred Corrections (SDC) Time Integration Technique and the Piecewise Parabolic Method (PPM)

We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge-averaged quantities, which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [1]. However, [1] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [1]. The method is fourth order (both in space and time) for smooth flows, and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.

A Regularized Newton Method with Correction for Unconstrained Convex Optimization

In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC2, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.

Determinants of Risky Sexual Behaviour among Inmates in Katsina Correctional Service: A Mixed Methods Study

Background: Incarceration does not vitiate sexual desire. Therefore, sexual activities occur behind bars, regardless of the stringent rules in correctional institutions. However, little has been documented about risky sexual behaviors, determinants, and experiences among inmates of correctional institutions in Katsina State, Nigeria. The study determined the sexual practices, prevalence, and determinants of risky sexual behaviors among prison inmates in Katsina. Methodology: A descriptive cross-sectional design with concurrent mixed methods of data collection was used to interview 216 inmates using a semi-structured questionnaire supplemented with 22 in-depth interviews. Result: Most (94%) respondents were male, almost half (44.4%) had secondary education, more than half (55.1%) were engaged in business or trading before incarceration, and the majority (75.9%) were awaiting trial. Nearly all inmates (98.6%) reported having sexual desire. Drug use (80.1%) and unprotected sex (79.2%) were quite common but sexual violence was low (7.4%). The number of sexual partners of respondents remained a significant predictor of sexual activity. Inmates who had one (1) or no sexual partner were 64% less likely to engage in risky sexual activity within the confines of the prison (AOR = 0.36, 95% CI = 0.20 - 0.63, p = 0.01). Qualitative interviews revealed the denial of occurrence of sexual activity in prison despite sexual desire felt by inmates;loneliness, poverty, and curiosity as motives for sexual relations;denial of occurrence of sexual violence in prison;and drug use and use of unsterilized sharps as risky sexual behaviors. Conclusion: Despite the disciplinary action meted out on inmates, prisoners still engaged in a range of risky sexual behaviors. Conjugal visitations for married inmates could be considered to reduce sexually deviant and risky alternatives of relieving sexual desire among prisoners.

基于弯矩修正法的浅水区海底直铺管道允许悬跨长度计算

海底管道悬空问题是管道工程建设中经常遇到的重要问题,当管道的悬跨长度达到一定值时,管道较容易失稳,而悬空油气管道失稳破坏导致的后果往往非常严重,因此需要对悬空的海底管道进行定期的维护和处理,但由于海上作业难度大,针对悬空管道的治理成本非常高,因此可考虑对处于悬空但在安全允许悬空范围内的管道暂时不进行加固,此时就需要计算管道的允许悬跨长度,为管道的治理提供依据。由于我国油田大多建设在近海地区,因此在考虑管道的悬空问题时需考虑浅水区波浪的特点。本文考虑浅水区波浪的非线性影响,推导得到浅水区波浪场内任意一水质点的水平流速和竖向流速计算公式,并根据该公式和Morison方程,进一步建立了管道悬跨水动力载荷的表达式,最后基于弯矩修正法,提出浅水区平铺海底管道允许悬跨长度计算公式。根据工程实例,结合本文研究,计算得到该工程所在海区平铺管道允许悬跨长度。

掏土孔应力扰动法下的塑性区范围研究

针对普通浅层掏土法下倾斜建筑回倾速度慢、沉降不均匀的问题,提出掏土孔应力扰动法。在岩石力学的弹性圈和塑性圈应力解中引入修正系数,得到掏土孔应力扰动法下的塑性区半径计算公式。在进行现场掏土孔周应力扰动试验时,采用地锚反压的形式模拟上部建筑荷载,利用长钉在掏土孔周围进行深度为50 mm的螺旋扰动,通过测量应力扰动前后的孔周土体应力并结合有限元模拟结果,得到实际塑性区范围,验证了塑性区半径公式的正确性。结果表明:当掏土孔半径为100 mm,应力扰动范围为孔径的1/2时,塑性区范围扩大30%~40%,掏土孔应力扰动法对于扩大塑性区范围、加快建筑纠倾速度具有工程应用价值。